NL2008392C2

NL2008392C2 - Method for examining the interior material of an object.

Info

Publication number: NL2008392C2
Application number: NL2008392A
Authority: NL
Inventors: Xavier Georges Jos Deleye; Rchens Lars H; Andries Gisolf
Original assignee: Ntgen Tech Dienst B V R
Priority date: 2012-03-01
Filing date: 2012-03-01
Publication date: 2013-01-03
Also published as: NL2008392A

Description

Title: Method for examining the interior material of an object.

The present invention relates to a method for examining the interior material of an object from a surface of the object using ultrasound for example having a frequency of at least 100 kHz, wherein the method comprises the steps of: 5 a. transmitting at least a first ultrasound signal by at least one first ultrasound transmitter of a predetermined group of ultrasound transmitters to the interior material of the object where in the interior material of the object reflections and/or diffractions of the first ultrasound signal occur, b. receiving reflections and/or diffractions of the first ultrasound signal 10 from the interior material of the object using a plurality of ultrasound receivers of a predetermined group of ultrasound receivers which plurality of ultrasound receivers are acoustically coupled to the outer surface of the object at positions which are distributed in at least one dimension of the outer surface of the object, wherein, with each of the plurality of ultrasound 15 receivers, a receiving signal is generated from the received reflections and/or diffractions of the at least first ultrasound signal from the interior material of the object, c. processing in combination the receiving signals generated by the plurality of the ultrasound receivers in order to determine, according to the 20 principle of inverse wave field extrapolation, where in the interior material of the object reflection and/or diffractions of the transmitted first ultrasound signal occur.

The invention also relates to a system for carrying out such a method. Such a method and system are known from amongst others WO 2005/068995 25 Al. This known method and system is referred to as IWEX (Inverse Wave field Extrapolation). It is also known from NL 2007348 that the processing in combination of the receiving signals can be sequential or in parallel.

Conventional Ultrasonic Testing (UT) methods are applied worldwide to inspect the quality of welds and objects. These techniques rely on ultrasound 2 beams to insonify the volume under inspection. Examples of those techniques are: Pulse Echo (PE), Tandem technique, Creep wave or Time of Flight Diffraction (ToFD). Recently, Phased Array (PA) probes and techniques have emerged, providing another type of inspection visualization called sector scans 5 (SS, be it sectorial or linear). These techniques are based on the assessment of either reflections (PE, Creep, Tandem) or diffractions (ToFD) generated in the inspected object. PA sector scans generally rely on reflection, although diffraction signals are used sometimes as weh.

Regardless of the mechanisms they rely on, the position and 10 characterization of the defect is based on the assessment of the amphtude, arrival time and phase (for ToFD) of the received signal. However, under certain circumstances (unexpected defect orientation or weld geometry), these parameters can be modified in such a way that misinterpretation of the measured data arises.

15 Additionally, the inspection quality depends on the skills of the user: experienced operators will have in general more rehable results than novice inspectors.

A novel approach to UT is to image the region of interest directly. This is achieved by processing signal amphtude, arrival time and phase 20 automatically, where the output is an image of the inspection volume. This largely hmits errors by object geometry and human factor as less prior knowledge is used.

A known proposition for the imaging of objects is in the above referred to as Inverse Wave field Extrapolation (IWEX). In IWEX, the detected wave field 25 can be traced back from the received signals to the positions where it came from, particularly the positions of virtual sources that arise due to the reflections and/or diffractions of the ultrasound supphed to the object. In the case of an examination of a weld (e.g. of a pipeline or a plate), a virtual source may be the position of a welding defect. The receiving signals are the starting 30 point of the inverse wave field extrapolation. On the basis of the receiving 3 signals, the time can be mathematically reversed. With the inverse wave field theory, the detected wave field is traced back to the position where it came from, namely the position of the virtual sources. The wave theory takes into account both the amplitude and the delay time of the signal. The process of 5 tracing back the wave field measured is called the inverse wave field extrapolation.

Practically, this may mean that for a received signal on position X outside the object, it is calculated back in time which portion of the received signal may have been caused by a reflection and/or diffraction on position Y 10 within the object. This portion of the signal is characterized by its amplitude and phase. Thus, in this calculation, the amphtude, phase and arrival time (for calculating which portion of the signal may belong to position Y) of the received signal is taken into account. This portion of the signal which belongs to position Y is calculated for each received signal. The portions of the received 15 signals (expressed in amplitude and phase) which belong to position Y are summed to obtain a characterizing value (for example also expressed in an amplitude and a phase) for position Y. This process is carried out for a plurality of positions Y, Y’, Y”, etc within the object. The combined result (all characterizing values) for all of these positions provides the basis for making 20 an image of the interior of the object. Each position Y, Y, Y”, etc may for example be represented by a pixel of the image wherein for example the intensity or color of the pixel corresponds to the amphtude of the characterizing value.

IWEX is a promising hightech imaging technique. However, the 25 algorithm has a number of limitations. For example, if a probe comprises the at least one transmitter and the receiver and the probe is located near a front wall surface of the object, these are: 1) No clear imaging of the area directly below the front wall is possible.

This can be considered as the ‘near field’ of the probe, although this does 30 not match the exact definition given for ultrasound beams.

4 2) Only the volume below the probe (comprising the transmitters and the receivers) is imaged, so volumes adjacent to the probe are not assessed. This is a problem when inspecting e.g. a weld, as the volume of interest is below the weld cap, exactly the position where no probe can be placed 5 easily without removing the weld cap.

3) If defects are positioned perpendicularly to the surface, then only the tip diffractions caused by the defect will be imaged (exactly equivalent to ToFD). The only way to discover if both indications are linked is by assessment of their individual phase.

10

For insonification and imaging of defects, a number of choices can be made.

For instance, IWEX can be based on direct insonification using longitudinal spherical waves. Hence, imaging of the back wall of the object (this is a wall of the object laying opposite to a front wall of the object where in this example 15 the probe (comprising the transmitters and receivers) is situated near the front wall; the front wall and the back wall each belong to the surface of the object.) and of defects that are not located near the edges of a probe aperture provides good results. However, defects directly below the probe are less well imaged by IWEX. The main reason for this is the fact that for very shallow defects travel 20 times become very short and illumination angles become very high, resulting in poor depth resolution in this area. In addition, due to cross-talk between the channels, the very early arrivals are contaminated with electronic disturbances.

An object of the invention is to provide a solution to at least one of the 25 problems referred to above.

According to the invention, it holds that the method is characterized in that, the object is provided with at least one predetermined reflection surface wherein in step a. the first ultrasound signal is transmitted such that it reflects at least one time within the object on the at least one predetermined 30 reflection surface before it reaches a first predetermined position in the 5 interior of the object and may provide reflections and/or diffraction at the first predetermined position; and/or wherein in step a. the first ultrasound signal is transmitted and in step b. ultrasound is received such that if in step b. reflections and/or diffractions at the first predetermined position from the first 5 ultrasound signal are received, the first ultrasound signal after that it has provided the reflections and/or the diffraction at the first predetermined position, at least one time reflects within the object on the at least one predetermined reflection surface before it is received by the plurality of ultrasound receivers wherein in step c. the receiving signals are processed 10 according to the principle of inverse wave field extrapolation , while in the inverse wave field extrapolation which is carried out in the processing, said at least one reflection on the at least one predetermined reflection surface is taken into account.

Because of the use of the at least one reflection surface in step a.

15 and/or in step b. wherein in step c. the receiving signals are processed according to the principle of inverse wave field extrapolation while in the inverse wave field extrapolation, which is carried out in the processing, said at least one reflection on the at least one predetermined reflection surface is taken into account, it is made possible that the first predetermined position 20 lies in an area from which it was indicated above that no clear imaging was possible. Also defects as mentioned above under 3) may now be detectable if the proper reflection surface is used as will be explained hereafter.

It is noted that according to the invention the acoustical coupling of the receivers with the surface may be directly or via an intermediate medium, like 25 a wedge, a flexible cushion or a fluid layer. Also the at least one transmitter may be acoustically coupled to the surface of the object and this may be directly or via an intermediate medium, like a wedge, a flexible cushion or a fluid layer.

It is also noted that the surface of the object may include a front wall 30 and/or back wall of a plate which front wall and back wall extend parallel to 6 each other. The surface of the object may include an inside wall and/or an outside wall of a pipe etc. This means that the at least one transmitter and receivers may be acoustically coupled with any of these walls and any of the walls may form the at least one predetermined reflection surface.

5 It is also noted that the processing in combination with the receiving signals can be sequential or in parallel. Furthermore it is noted that the processing according to the principle of inverse wave field extrapolation includes techniques wherein the inverse wave field extrapolation is calculated on the basis of mathematical models which provide approximations of the 10 physical reality. Generally it includes calculating back in time by means of some algorithm to determine which portion of the received signal may have been caused by a reflection and/or diffraction on the first predetermined position within the object. This portion of the signal may be characterized by its amplitude or by its amplitude and phase. It is also noted that according to 15 the present invention the first predetermined position in the interior of the object may also include a position at an outer surface of the object where reflections and/or diffractions occur.

In accordance with a practical embodiment of the method it holds that the object is in the form of a plate having a first outer wall and a second outer 20 wall lying opposite to each other wherein in step a. the ultrasound signals are transmitted into the object from the first outer wall of the object and wherein in step b. the ultrasound signals are received from the object at the first outer wall of the object and/or the second outer wall of the object wherein the second outer wall of the object forms a predetermined reflection surface which is used 25 in step a. and/or in step b.

Preferably, it holds that in step a. the first ultrasound signal is transmitted into the object via a wedge, particularly a plastic wedge. In certain embodiments the wedge is designed such that the first ultrasound signal in the object comprises mainly shear waves. The wedge is thus situated between the 30 at least one transmitter which is used in step a. and the object.

7

The invention will now further be explained with reference to the following drawings:

Fig. la shows a cross section in axial direction of two parts of a pipeline connected to each other by means of a weld and an apparatus according to the 5 invention for carrying out a method according to the invention;

Fig. lb shows a cross section in radial direction of the pipeline according to Fig. la together with the apparatus according to the invention shown in Fig. la;

Fig. 2a shows a cross section in axial direction of two parts of a pipeline 10 connected to each other by means of a weld, and a second embodiment of an apparatus according to the invention for carrying out a method according to the invention;

Fig. 2b shows a cross section in radial direction of the pipeline according to Fig. 2a together with the apparatus according to Fig. 2a; 15 Fig. 2c shows a view in the direction of the vector V in Fig. 2a;

Fig. 3 shows an illustration of the IWEX measurement concept. Top row: element 16.1 transmits a spherical wave that is reflected and diffracted towards the receiving elements 16.i (i=l-n), resulting in the shot record at the right hand side. Horizontal axis = element number, vertical axis = time 20 sample, and intensity = signal amplitude. Middle row: idem for element 16.2. Bottom row: idem for element 16.n;

Fig. 4 shows an example of IWEX processing for an image point positioned at a healthy part of the object. Top left: Measurement overview and positions of transmitter T (star), image point A (square) and receiver R (dot).

25 Top right: shot record corresponding to transmitting element 16.50, where the signal of receiving element 16.59 is the dotted line and shown at the bottom right of the figure (with arrival time Har and amplitude Atar). Bottom left: temporary output image with Atar after correction at the position of A;

Fig. 5 shows an example of IWEX processing for an image point 30 positioned at a defect boundary. Top left: Measurement overview and positions 8 of transmitter T (star), image point D (square) and receiver R (dot). Top right: shot record corresponding to transmitting element 16.50, where the signal of receiving element 16.59 is the dotted line and shown at the bottom right of the figure (with arrival time tTDR and amplitude Atdr). Bottom left: temporary 5 output image with Atdr after correction at the position of D;

Fig. 6 shows an illustration of IWEX imaging. Top left: measurement setup; top right: illustration of all sources (stars), receivers (dots, superimposed on the stars in this example) and imaging point (squares); bottom: IWEX output image superimposed on object; 10 Fig. 7 shows imaged wave arrivals for IWEX, SKIWEX, TIWEX and TRIWEX respectively wherein T = transmitter (source) element, D = image point, R = receive element.

Fig. 8 shows an illustration of the path differences between IWEX (left hand side) and SKIWEX (right hand side); 15 Fig. 9 shows an illustration of the path differences between IWEX (left hand side) and TIWEX (right hand side);

Fig. 10 shows an illustration of two possible paths for TRIWEX;

Fig. 11a shows an illustration of the IWEX direct (dotted arrows), SKIWEX (solid arrows) imaging of a defect at position D;

20 Fig. lib shows an illustration of TIWEX (dashed arrows) and TRIWEX

(solid arrows) imaging of a defect at position D;

Fig. 12 shows ray paths for TIWEX (coinciding source and receiver);

Fig. 13 shows geometry and coordinate frames for back-projection of sources and receivers along wedge (dot-dash line) onto a new virtual source 25 location A' and a new virtual receiver location A along the front wall of the steel plate;

Fig. 14 shows transmission coefficients Tpp and Tps (real and imaginary part) for a plastic/steel interface; 9

Fig. 15 shows Left: back-propagation kernel in k / / domain (Grange is from 0 to 2 kNyquist), Middle: full cosine square tapered k / /filter, Right: back-propagation kernel after k / f filtering;

Fig. 16 shows the four different back-propagation trajectories within an 5 object to be inspected from sources and receivers, with and without back-wall skips;

Fig. 17 shows a synthetic example of three point defects along the bevel of a weld, illuminated in TIWEX mode with shear waves;

Fig. 18 shows the reflection coefficient shear to shear for a steel/air 10 interface; and

Fig. 19 shows TIWEX geometry for given source position, receiver position and image point location D.

Fig 20 shows left; imaging of the synthetic data-set of Fig 17.with the application mask limiting the maximum illumination angle to 100° and shows 15 right: imaging the same dataset without the application of the illumination mask.

Fig 21 shows a pipe whereto an embodiment of a method according to the invention is applied.

Fig 22a en 22b shows an object such as a plate whereto an embodiment 20 of a method according to the invention is applied; and

Fig 23a en 23b shows an object such as a pipe whereto an embodiment of a method according to the invention is applied;

In Fig. la, reference numeral 1 designates an object comprising a first 25 pipeline 2 and a second pipeline 4 and a circumferential weld 6 with which the first pipeline 2 and the second pipeline 4 are connected with each other. Each pipeline is provided with an outer surface 8 and an inner surface 10 between which interior material 12 is present. The circumferential weld 6 is likewise provided with interior material 12. The weld extends above the surface 8. This 30 extending portion is called a weld cap 52.

10

Figs, la and lb further show a system 14 for examining, from a surface of an object, in this example from the outer surface 8 of the pipehnes 2, 4, the interior material 12 of the object 1, particularly that part of the object that comprises the weld 6. The system 14 is provided with a group of ultrasound 5 receivers 16.i (i=l,2,3,...,n) arranged relative to each other according to a unidimensional array. This array extends in axial direction of the pipelines 2, 4. Here, the number n of receivers within the group is a natural number greater than or equal to 2. A practical value is for instance n=36. The system is further provided with at least one transmitter for supplying ultrasound to the 10 interior material 12 to be examined. In this example, each ultrasound receiver 16.i is also designed as an ultrasound transmitter 16.i. Thus the device is also provided with a group of transmitters. The ultrasound transmitter and receiver elements 16.i, herein also referred to as ultrasound feelers or transducers or elements 16.i, are connected with a control-unit/control means 15 22 comprising signal-processing means via respective lines 20.i. The system 14 is further provided with transport means 24 known per se, which are diagrammatically indicated in Fig. lb, to move the unidimensional array of ultrasound transmitter and receiver elements 16.i in radial direction around the object 1.

20 The operation of the system is as follows. Using, for instance, all ultrasound transmitter and receiver elements 16.i, ultrasound (also referred to as an ultrasound signal) is supplied to the interior material 12 of the object 1 in a pulsed manner. For this purpose, the ultrasound transmitter and receiver elements are acoustically coupled to the interior material. In practice, this can 25 be realized by applying a liquid film to the outer surface of the object, while the ultrasound transmitter and receiver elements are placed so as to abut on the surface of the object 1. The ultrasound supplied has a frequency higher than 100 kHz. The transmission of the ultrasound is controlled by a control-unit 22 comprising the signal-processing means, such that, in this example, the 30 ultrasound transmitter and receiver element 16.1 transmits first at a pulse 11 repeat frequency which is, for instance, higher than 25 Hz. The ultrasound will propagate through the material of the object 1 and reflection and/or diffraction will occur when the sound passes or hits a transition in the material (such as walls and/or welding flaws). Such a reflection and/or diffraction can be taken 5 as a new virtual source, the sound energy of which in turn propagates through the material. With each of the unidimensional array of ultrasound transmitter and receiver elements 16.i, the ultrasound coming from the "new virtual sources" is in turn received. The receiver elements generate corresponding receiving signals. Each virtual source consists of a collection of point sources 10 whose positions can be determined. Therewith, the position, magnitude and shape of the respective virtual source can also be determined. Thus, each ultrasound receiver 16.i generates a receiving signal which is supplied to the control unit/means 22 which comprises signal-processing means. The receiving signals are recorded during a certain period of time. This period is, for 15 instance, chosen such that a virtual source located in the interior material 12 at a maximum distance from the ultrasound transmitter and receiver elements 16.i is still received before a next ultrasound pulse is supplied to the interior material of the object. This may, for instance, be a defect in the weld 6 located near the inner surface 10 of the pipelines 2,4. It may also be a defect located 20 between the weld and one of the pipelines near the inner surface 10. This is because the ultrasound signal first needs to propagate from the ultrasound transmitter and receiver elements 16.i to the respective flaw and then propagate back from the flaw to the ultrasound transmitter and receiver elements 16.i due to diffraction and/or reflection of the sound as a result of the 25 flaw. Then transmitter 16.2 starts transmitting as explained for transmitter 16.1. Again all receivers 16.1-16.n are used for receiving ultrasound signals and the received signals are stored for processing. Subsequently the whole process is repeated for transmitters 16.3- 16.n.

Then, the ultrasound receivers and transmitters 16.i are moved in the 30 direction of the arrow 26 using the means 24. The speed of the movement may 12 for instance be such that, between two series of ultrasound pulses for all transmitters, the linear array is moved over a distance equal to the size of the ultrasound receivers of the linear array. However, other, for instance smaller, distances are also possible. One possibility is a distance of a few millimeters.

5 All this means that, in this example, when the linear array has been moved over a distance d, again the whole process wherein the transmitters 16.1-16.n subsequently transmit ultrasound signals into the object wherein each time all receivers 16.1-16.n are used for generating receiving signals is repeated. Completely analogously, using each of the ultrasound receivers 16.i, a 10 receiving signal is generated which is supplied to the signal-processing means. So, the ultrasound feelers are acoustically coupled to the outer surface of the object at positions which are, in this example at different times, distributed in two dimensions of the surface of the object for generating receiving signals. That, in this example, the respective positions are distributed in two 15 dimensions of the surface of the object at different times and not at one point in time, is, on the one hand, the result of the receivers 16.i being arranged relative to each other according to a unidimensional array and, on the other hand, the result of the receivers being moved as discussed hereinabove. Were the receivers 16.i not moved, then the respective positions would be distributed 20 in one dimension of the surface not only at one point in time but at different times.

The receiving signals coming from the receivers which are distributed in two dimensions of the surface are processed in combination in order to determine, according to the principle of the inverse wave field extrapolation, 25 where in the interior material 12 of the object 1 reflections and/or diffractions of the ultrasound occur. The result gives the positions of the above-mentioned virtual sources. In the case that a weld of a pipeline is examined in this manner, information can be obtained about the position, shape and magnitude of a possible defect. This is because a defect forms a virtual source and 30 accordingly a collection of virtual point sources, the positions of which are 13 determined by the position, shape and magnitude of the defect. So, this information in effect forms a three-dimensional image of the material examined. Optionally, further information can be obtained about the nature of the defect. For instance, of a weld of a pipeline comprising a cavity and 5 accordingly a defect, it can be determined whether the cavity is filled with air, liquid or copper.

On the basis of the receiving signals the time can be mathematically reversed. With the wave theory, the detected wave field is traced back to the position where it came from, namely the position of the virtual sources. In this 10 example, these virtual sources may, for instance, be welding defects. The wave theory takes into account both the amplitude and the delay time of the signal. The process of tracing back the measured wave field is called inverse wave field extrapolation and is known per se.

If the signals of the unidimensional array of receivers were only 15 processed when the receivers are at one single position, a reasonable resolution in axial direction would be obtained. In axial direction, the unidimensional array in effect functions as a lens which makes a "sharp" image in axial direction. However, in radial direction, the resolution is relatively poor. By now also processing receiving signals from ultrasound receivers displaced 20 relative to each other in radial direction, the resolution in radial direction can be improved. Then, the "effect of a lens" is also present in that direction. The result is that, with the signal-processing means of the control-unit 22, magnitude, position and even the shape of a virtual source and accordingly the magnitude, position, shape and nature of, for instance, defects in the weld of 25 the object 1 can be detected. More in general, the position, shape, magnitude and nature of "irregularities" in the interior material can be determined.

In this example, the receiving signals may be processed in real time.

The processing of the receiving signals is carried out such that the result of the processing can be imaged on a display. For this purpose, the apparatus is, in 30 this example, provided with a display 29. Now the position, magnitude, shape 14 and nature of each virtual source are known, the information obtained about the virtual sources can be imaged on the display in various manners. For instance an, in perspective, three-dimensional image of the interior material can be made. Here, one looks through the object from outside, as it were.

5 However, it is also possible to have the point of view from which the material is imaged inside the material. The point of view and the direction of view may then be chosen by an operator, for instance using a joystick. One travels through the material, looking around, as it were. Such variants are understood to be within the framework of the invention. However, the receiving signals 10 may also be saved in order to be processed later.

According to an alternative embodiment of the invention, it holds true that the ultrasound feelers (also referred to as transducers) are arranged relative to each other according to a two-dimensional array. All this is shown in Figs. 2a and 2b. The apparatus according to Figs. 2a, 2b and 2c is provided 15 with a two-dimensional array of ultrasound receivers (16.i.j. (i=l,2,3,...,n; j=l,2,3...,m). Here, it holds true that n and m are greater than or equal to two. Alternatively other two-dimensional distributions of ultrasound feelers can be used, like concentric circles or daisy shape. Because now a two-dimensional array of ultrasound receivers is present which are, in this case, distributed in 20 two dimensions of the outer surface of the object at one and the same time, the ultrasound receivers need not be moved along the surface now for obtaining receiving signals which can be processed in combination according to the principle of inverse wave field extrapolation as discussed hereinabove. In this example, each ultrasound receiver 16.i.j. is also designed as an ultrasound 25 transmitter 16.i.j. Such a combined transmitter/receiver is also referred to as a feeler or transducer. Completely analogous to what has been discussed for Fig. 1, all transmitters generate one after the other, for instance, a pulsed ultrasound signal. This involves n*m physical experiments. Of each pulse, diffractions and/or reflections of the ultrasound signal at transitions in the 30 material are measured using the ultrasound receivers 16.i.j., while each 15 ultrasound receiver 16.i.j. generates a receiving signal which is supplied to the signal-processing means for determining, according to the principle of inverse wave field extrapolation, where in the interior of the material reflections and/or diffractions of the ultrasound occur. As said, these reflections and/or 5 diffractions can be caused by transitions in structure or density in the interior material 12. In the case of metal pipelines, these may be transitions between different grid structures of the material, a transition between different types of material, and, with the weld 6, defects of the weld. A defect may, for instance, comprise a space between weld and pipeline which is not filled with welding 10 material and therefore forms a transition in the interior of the material which will cause diffraction and/or reflection of the ultrasound. This "hollow space" or inhomogeneity in the material will then behave like a virtual source as discussed hereinabove.

When receiving signals are processed which come from ultrasonic 15 receivers distributed in two dimensions over the surface of the object, an actual three-dimensional image of the interior and surface of the object can be obtained.

In the apparatus according to Fig. 2a, for examining for instance a space 28 (also referred to as a predetermined area), it is not necessary that the 20 two-dimensional array of receivers 16.i.j. moves along the outer surface. If one wishes to examine, for instance, area 30 in addition to area 28, then, the two-dimensional array can be moved to the area 30 if desired. So, in the case that a two-dimensional array is used for a pipeline, it is not necessary to surround the whole pipeline using ultrasound receivers 16.i.j. What is 25 sufficient is, for instance, providing ultrasound receivers distributed over a radial angle smaller than 360 degrees, preferably about 180 degrees. Of course, this does not exclude the possibility that the ultrasound receivers are provided over a radial angle of 360 degrees around the pipeline and the weld.

In that case, the whole circumferential weld can be examined in one go.

16 A possible practical embodiment of the IWEX principle may be further conceptually described as follows.

The IWEX method employs a PA probe 17 and is conceptually described hereafter. A full derivation of a possible IWEX algorithm (including 5 discussions on the imaging condition and the Green’s function) can be found in the PhD thesis of Niels Pörtzgen: Imaging of Defects in Girth Welds Using Inverse Wave Field Extrapolation of Ultrasonic Data, 2007, publication date 2007-11-06.

The practical IWEX concept can be explained as follows: one element is 10 used as a source to transmit a spherical elastic wave, while all array elements are used as receivers. This experiment is repeated for the next transmitting element, until all elements have been used as transmitters independently (see fig. 3 for a unidimensional array of elements each of which is a transmitter and a receiver. The collection of elements forms in this example a probe 17).

15 The obtained dataset consists of time signals for each transmitter-receiver combination.

The obtained dataset is then used to solve the Rayleigh integral in the IWEX algorithm. In this computation, signals are corrected for phase differences and amplitude (in terms of spherical spreading). Although current 20 IWEX algorithms operate in the space-frequency domain, for the sake of clarity the IWEX data-processing is demonstrated in this section in the space-time domain (see figure 4).

First, source and receive elements are chosen. In this example, elements 16.50 and 16.59 have been selected as transmitter and receiver, respectively.

25 These could for example be the transmitter/receiver 16.50 and 16.59 from figures la-lb. Then, an image point in the volume is chosen; for instance point A, which is positioned on a location without defect. In the dataset, the time trace corresponding to transmitter 16.50 and receiver 16.59 is selected. After correction for amplitude and phase differences (using the Rayleigh integral), 30 the amplitude corresponding to time of flight Uar is stored in a temporary 17 matrix, at coordinates (xa, za). As there is no defect in point A, the amplitude Atar is low; and hence a small value is stored in the image matrix.

Figure 5 shows the result of performing previous approach for a point D located at a defect position: in the signal corresponding to transmitter 16.50 5 and receiver 16.59, the amplitude at time tTDR is high; and so a high value is stored in the image matrix.

Imaging with IWEX is achieved by repeating the technique described above for preferably all transmitters and receivers in the PA probe and for all image points. The final intensity of each image point is the sum of the source- 10 receiver amplitudes for that point. This is illustrated in fig 6. where the final IWEX image 19 has been superposed to the object 1 under inspection.

As discussed in the introduction, IWEX is a promising high tech imaging technique. However, the algorithm has a number of limitations. These are: 15 1) No clear imaging of the area directly below the front wall is possible.

This can be considered as the ‘near field’ of the probe, although this does not match the exact definition given to ultrasound beams.

2) Only the volume below the probe is imaged, so volumes adjacent to the probe are not assessed. This is a problem when inspecting a weld, as the 20 volume of interest is below the weld cap 52, exactly the position where no probe can be placed easily without removing the weld cap 52.

3) If defects are positioned perpendicularly to the surface, than only the tip diffractions caused by the defect will be imaged (exactly equivalent to ToFD). The only way to discover if both indications are linked is by 25 assessment of their individual phase.

For insonification and imaging of defects a number of choices can be made. For instance, IWEX is based on direct insonification using longitudinal spherical waves. Hence, imaging of the back wall and of defects that are not 30 located near the edges of a probe aperture provides good results. However, 18 defects directly below the probe are less well imaged by IWEX. The main reason for this is the fact that for very shallow defects travel times become very short and illumination angles become very high, resulting in poor depth resolution in this area. In addition, due to cross-talk between the channels, 5 the very early arrivals are contaminated with electronic disturbances.

As discussed above, the area in the object directly below the transducer elements is difficult to image due to channel cross-talk. To compensate for this 'blind area', in according with an embodiment of the present invention an IWEX spin-off algorithm has been developed. This code, called skip-IWEX 10 (SKIWEX), considers the ultrasound signals reflecting on an outer wall 10 of the object (also referred to as a predetermined reflection surface of the object 1), effectively using the outer wall 10 as a mirror to illuminate shallow defects from below. Hence, the opposite side (i.e. ‘back wall side’ or ‘far side’) of defects is imaged (see SKIWEX in figures 7 and 8). In terms of physics, the 15 improvement comes from the much longer travel times and much smaller illumination angles resulting in improved depth resolution (compare IWEX and SKIWEX in figure 8).

This technique is also useful when imaging a volume with a gap between the probes. In practice, this gap is caused by the weld cap 52, on 20 which no probe can be placed. The use of the back wall as a mirror extends the illuminated volume in the weld area. Hence, SKIWEX should solve limitations 1) and 2) mentioned above.

It is noted that in figures 7, 8 only one transmitter and only one receiver is shown for simplicity. The transmitter T may for example be transmitter 25 16.1.3 from figure 2a and the receiver R may for example be receiver 16.1.6 from figure 2a. For calculating the complete image, all transmitter and receiver combinations can be used per predetermined position D as explained for figure la-6. It is most efficient that the transmitters transmit one after the other. When one transmitter transmits all receivers are used for receiving. In 30 that case each receiver generates a receiving signal. Moreover in that case 19 during the transmission of the single transmitter there are a plurality of transmitter-receiver combinations used at the same moment in time corresponding to the single transmitter and the plurality of receivers. After that a next single transmitter may be used while at the same time all receivers 5 are used for generating receiving signals. This process can be repeated for the other transmitters.

In the following, the use of only one transmitter and receiver combination will be explained for several embodiments according to the invention. It will be explained how for such combination the receiving signal 10 from receiver R can be processed if the signal was transmitted by transmitter T. For other transmitter and receiver combinations the processing will be the same. Also for other predetermined positions D the processing will be the same. How other transmitter and receiver combinations can be obtained has already been explained on the basis of figures la-6.

15 Thus, in general it holds for the method for examining the interior material of an object (2, 4, 6) from a surface (8) of an object using ultrasound having a frequency of at least 100 kHz, that the method comprises the steps of: a. transmitting at least a first ultrasound signal by at least a first ultrasound transmitter (16i; 16.i.j) of a predetermined group of ultrasound 20 transmitters to the interior material of the object (2,4,6) where in the interior material of the object reflections and/or diffractions of the first ultrasound signal occur, b. receiving reflections and/or diffractions of the first ultrasound signal from the interior material of the object using a plurality of ultrasound 25 receivers of a predetermined group of ultrasound receivers (16.i; 16.i.j) which plurality of ultrasound transmitters are acoustically coupled to the outer surface (8) of the object at positions which are distributed in at least one dimension of the outer surface of the object, wherein, with each of the plurality of ultrasound receivers (16.i; 16.i.j), a receiving signal is generated from the 30 received reflections and/or diffractions of the at least first ultrasound signal 20 from the interior material of the object, c. processing in combination the receiving signals generated by the plurahty of the ultrasound receivers in order to determine, according to the principle of inverse wave field extrapolation, where in the interior material of 5 the object reflection and/or diffractions of the transmitted first ultrasound signal occur. This has already been explained on the basis of the example figures la-6 above.

It is also explained on the basis of figures la-6 above that it may hold that step a. is repeated for another ultrasound transmitter from the first group 10 of ultrasound transmitters wherein step b. is repeated using a plurality of ultrasound receivers from the group of ultrasound receivers for each repeated step a. and wherein step c. is carried out on the bases of the collection of ultrasound receiving signals which are obtained in the steps b. which have been carried out. More particularly it holds in this explained embodiment that 15 step a. is repeated for another ultrasound transmitter from the first group of ultrasound transmitters wherein step b. is repeated using a plurahty of ultrasound receivers from the group of ultrasound receivers for each repeated step a. and wherein step c. is carried out for each repeated step b. Thus in that example for one predetermined position, step c. is repeated for another used 20 receiver and transmitter combination.

And it may thus also hold that step a. is repeated for each ultrasound transmitter from the group of ultrasound transmitters wherein step b. is carried out using a plurahty of ultrasound receivers from the group of ultrasound receivers for each step a. which has been carried out wherein step 25 c. is carried out on the bases of the cohection of ultrasound receiving signals which are obtained in the steps b. which has been carried out. More particularly it may hold in the latter case that step c. is carried out for each step b. which has been carried out. Thus in that example for one predetermined position step c. is repeated for each used receiver and 30 transmitter combination. The advantage is that such an algorithm may be 21 relative simple because it is based on repeating the same calculation for each used transmitter-receiver pair as is also explained on the basis of figures 4-6.

Also it may thus hold that in step b. each ultrasound receiver of the group of ultrasound receivers is used for receiving the ultrasound signals as is 5 explained on the basis of figures 4-6. Moreover said steps c. may moreover be repeated for another predetermined position as is also explained on the basis of figure 6. Again for such another predetermined position step c. may be carried out for each used transmitter-receiver combination in steps a. and b.

According to the invention, it generally further holds that the object is 10 provided with at least one predetermined reflection surface (8, 10) wherein A. in step a. the first ultrasound signal is transmitted such that it reflects at least one time within the object (2, 4) on the at least one reflection surface (8, 10) before it reaches a first predetermined position (D) in the interior of the object and may provide reflections (this is true for the example of SKIWEX as shown 15 in figures 7, 8 ) and/or diffraction at the predetermined first position and/or wherein B. in step a. the first ultrasound signal is transmitted and in step b. ultrasound is received such that if in step b. reflections and/or diffractions at the first predetermined position from the first ultrasound signal are received, the first ultrasound signal after that it has provided the reflections and/or the 20 diffraction at the first predetermined position , at least one time reflects within the material of the object on the at least one predetermined reflection surface before it is received by the plurality of ultrasound receivers (16.i; 16.i.j) (this is also true for the example of SKIWEX as shown in figures 7, 8) wherein in step c. the receiving signals are processed according to the principle of inverse wave 25 field extrapolation while in the inverse wave field extrapolation which is carried out in the processing, said at least one reflection on the at least one predetermined reflection surface is taken into account (this can be carried out in several ways as will be explained hereafter). The above general statement is not only true for SKIWEX as discussed above, but holds also for other 30 embodiments of the invention such as TIWEX and TRIWEX to be discussed 22 later. More particularly A. and B. are both used in SKIWEX and TRIWEX. In TIWEX A. or B. is used as will be explained later. In figure 7, 8 the point D is the predetermined position which lies in the predetermined area 28 to be investigated.

5 In accordance with the invention, an area 28 to be investigated may now lie just below an outer surface of the object or an area just below a weld cap 52. Assuming that in figure 8 the positions D1 and D2 lie in the predetermined area 28 to be investigated, it also holds that: A. in step a. the first ultrasound transmitter is positioned relative to the object such that the first ultrasound 10 signal after being transmitted reflects at least one time within the object on the at least one predetermined reflection surface (10) before it reaches the first predetermined position (Dl) in the object and may provide reflections and/or diffraction at the first predetermined position and/or D. wherein in step a. and step b. the first ultrasound transmitter and the plurality of ultrasound 15 receivers are positioned relative to the object such that if the first ultrasound signal provides reflections and/or diffraction at the first predetermined position , it will subsequently at least one time reflect within the object on the at least one predetermined reflection surface (10) before it is received by the plurality of ultrasound receivers. This is not only true for SKIWEX (in fact A. 20 and B holds for SKIWEX) as discussed, but also for other embodiments of the invention such as TIWEX (A. or B. hold for TIWEX) and TRIWEX (A. and B. hold for TRIWEX) to be discussed later.

More particularly, it holds that in step a. the first ultrasound transmitter is positioned relative to the object such that the first ultrasound 25 signal after being transmitted reflects at least one time within the object on the at least one predetermined reflection surface (10) before it reaches for the first, time the first predetermined position and may provide reflections and/or diffraction at the first predetermined position and/or wherein in step a. and step b. the first ultrasound transmitter and the plurality of ultrasound 30 receivers are positioned relative to the object such that if the first ultrasound 23 signal provides reflections and/or diffraction at the first predetermined position for the first time, it will subsequently at least one time reflect within the object on the at least one predetermined reflection surface before it is received by the plurahty of ultrasound receivers. This is not only true for 5 SKIWEX as discussed, but also for other embodiments of the invention such as TIWEX and TRIWEX to be discussed later.

For SKIWEX it thus holds that in step a. the first ultrasound signal reflects one time on the at least one reflection surface (10) and in step b. the first ultrasound signal reflects one time at a predetermined reflection surface 10 (10) of the object wherein preferable the reflection surface used in step a. is the same as the predetermined reflection surface used in step b. If the object is in the form of a plate (wherein a plate may also be a portion of a wall of a pipeline or a portion of a wall of two pipelines welded together) having a first outer wall (8) (also referred to as front wall) (see figures 7, 8) and second outer wall 15 (10) (also referred to as back wall) lying opposite to each other or wherein the object is a pipe having a first outer wall (also referred to as outside wall of the pipe) and a second outer wall (also referred to as inside wall of the pipe) lying concentric to each other, it holds that in step a. the ultrasound signals are transmitted into the object from the first outer wall of the object and wherein 20 in step b. the ultrasound signals are received from the object at the first outer wall (8) of the object wherein the second outer wall surface of the object forms a predetermined reflection surface which is used in step a. and/or in step b. This is not only true for SKIWEX as discussed, but also for other embodiments of the invention such as TIWEX and TRIWEX to be discussed later. In the 25 embodiment of figures 7, 8 the first outer wall 8 and the second outer wall 10 are each substantially flat surfaces extending substantially parallel to each other. This is not required. The walls need not to be flat and need not to be parallel to each other. Step c. can still be carried out provided that shapes and positions of the outer walls are known. This holds also for TIWEX and 24 TRIWEX and other special embodiments wherein predetermined reflection surfaces of the object are used in step a. and/or step b..

In the case that the object is such a plate it holds specifically for SKIWEX that in step a. only the second surface (10) is used as the at least one 5 reflection and that in step b. only the second surface (10) is used as a reflection surface.

More specially, if the object is in the form of a plate it holds, according to a special embodiment, that the predetermined area (28) lies relative close under the first surface, more particularly wherein the predetermined area 10 extends from the first surface towards the second surface over a distance (d) less than 50%, preferably less than 25%, more preferably less than 12.5% of the distance between the first and second surface. It is now also possible that the predetermined zone 28 lies below a weld cap 52 of the object (see figure 2a). Preferably it also holds that the first surface and the second surface are each 15 substantially flat surfaces extending parallel to each other. This makes the calculations for inverse wave field extrapolation easier. This also applies for other embodiments such as TIWEX and TRIWEX. Nevertheless, it is also possible to determine the second surface from the measurement itself and use the determined surface as a reflection surface for the further data processing. 20 It is also possible that the position of the reflection surface is known from other sources such as the manufacturer of the object.

The main drawback of the SKIWEX approach is that the back wall is required and, therefore, the plate thickness should be known, especially if it varies along the weld. Additionally, as the described embodiment for SKIWEX 25 uses compression waves, the shear waves should be preferably removed from the data. The latter is done using the shear wave removal technique which is described below. Alternatively, also a wedge can be used to mainly generate shear waves in the object, and use the shear waves also for SKIWEX.

Another embodiment of the invention is called tandem IWEX code 30 (TIWEX). The tandem approach uses a transmitter T that transmits a beam 25 towards a defect at an expected orientation, and a receiver R that records the resulting wave reflected by the wall 10 (see TIWEX in figure 7). In IWEX terms this translates to considering the waves that have traveled directly from the transmitting element to the defect, and have traveled back to the receiver 5 aperture via the wall (10) (see figure 7). Obviously, the opposite (transmission via wall (10) and direct reception) is also possible. The latter means that in figure 7 for TIWEX the position of the transmitter T and the receiver R may be interchanged wherein also the arrows which indicated the direction of travel of the transmitted ultrasound signal should be reversed. The main advantage of 10 this type of insonification is that reflection signals are optimally received for defects oriented (almost) perpendicularly to the wall 10. This is shown in figure 9 wherein IWEX and TIWEX can be compared. Hence, the final image will not only show two tip diffractions coming from the defect extremities, as it would for IWEX, but also the reflecting surface between the tips, which leads 15 to typically stronger signals and simplified interpretation and solves limitation number 3.

It follows for TIWEX that it holds, when used in the embodiment according to figures 1-6, that in step a. the first ultrasound signal is transmitted such that it reflects one time within the object on the at least one 20 predetermined reflection surface 10 before it reaches the first predetermined position D wherein subsequently in step b, if in step b. reflections and/or diffractions from the first ultrasound signal at the first predetermined position D are received, the first ultrasound signal after that it has provided the reflections and/or the diffraction at the first predetermined position does not 25 reflect within the object on any reflection surface 8, 10 of the object before it is received by the plurality of ultrasound receivers.

It also holds for TIWEX (if in figure 7 the transmitter T (16.i; 16.i.j) and receiver R (16.i; 16.i.j) are interchanged) that in step a. the first ultrasound signal is transmitted such that it does not reflect within the object at any 30 reflection surface 8, 10 of the object before it reaches the first predetermined 26 position D wherein subsequently in step b., if in step b. reflections and/or diffractions at the first predetermined position from the first ultrasound signal are received, the first ultrasound signal after that it has provided the reflections and/or the diffraction at the first predetermined position D does 5 reflect one time within the object on the at least one predetermined reflection surface 10 of the object before it is received by the plurality of ultrasound receivers R (16.i; 16.i.j).

It also follows for TIWEX that it holds, when used in the embodiment according to figures la, lb, 2a, 2b, and wherein the object is a plate or a pipe 10 as discussed that the second outer wall 10 forms the at least one predetermined reflection surface used in step a. and the second outer wall 10 forms the first predetermined reflection surface used in step b.

It also follows for TIWEX that it holds, when used in the embodiment according to figures la, lb, 2a, 2b, and wherein the object is a plate or pipe as 15 discussed that only the second outer wall (10) is used as the at least one reflection surface and that in step b. no reflection surface is used (the situation in figure 7); or in that step b. only the second wall (10) is used as the at least one reflection and that in step a. no reflection surface is used (the situation in figure 7 wherein the transmitter T and the receiver R are interchanged).

20 Another embodiment of the invention is called TRIWEX. An example for one pair comprising a transmitter S and receiver R is shown in figure 7 and 10 a. The signal of the transmitter T reflects first on a lower first reflection surface 10 before it enters a predetermined area 28 of interest wherein the signal is reflected and/or diffracted in predetermined position D. Then the 25 reflected and/or diffracted signal leaves the area of interest 28 and reflects first on an upper reflection surface and subsequently on the lower reflection surface before it is received by the receiver R. Of course the opposite wherein the transmitter T and the receiver R are interchanged and the direction of the arrows is reversed, is also possible as shown in figure 10b. There the signal of 30 the transmitter T reflects first on the lower surface 10 and then on the upper 27 surface 8 before it enters a predetermined 28 area of interest wherein the signal is reflected and/or diffracted in point D. Then the signal reflects once on the lower surface before it is received by the receiver R. The advantages of TRIWEX are: the area close to the first surface can now be examined without 5 the requirement that the transmitter or receiver is positioned very close to point D (in practice this is often restricted due to the width of the weld cap).

It follows for TRIWEX that it holds, when used in the embodiment according to figures la, lb, 2a, 2b, that in step a. the first ultrasound signal is transmitted such that it reflects one time within the object 1 on the at least 10 one reflection surface 10 before it reaches the first predetermined position D wherein subsequently in step b., if in step b. reflections and/or diffractions from the first ultrasound signal at the first predetermined position are received, the first ultrasound signal, after that it has provided the reflections and/or the diffraction at the first predetermined position D, does reflect one 15 time within the object on a first predetermined reflection surface 8 of the object and subsequently one time within the object on a second predetermined reflection surface 10 of the object before it is received by the plurality of ultrasound receivers R wherein preferable the at least one predetermined reflection surface 10 used in step a. is the same as one of the first 20 predetermined reflection surface 8 and the second predetermined reflection surface 10 used in step b. (this is the situation in figure 10a); or that in step a. the first ultrasound signal is transmitted such that it reflects one time within the object on a first predetermined reflection surface 10 of the object and subsequently one time within the object on a second predetermined 25 reflection surface 8 of the object before it reaches the predetermined position D wherein subsequently in step b., if in step b. reflections and/or diffractions from the first, ultrasound signal at the first predetermined position are received, the first ultrasound signal after that it has provided the reflections and/or the diffraction at the first predetermined position does reflect one time 30 within the object on the at least one predetermined reflection surface 10 of the 28 object before it is received by the plurality of ultrasound receivers R wherein preferable the at least one predetermined reflection surface 10 used in step b. is the same as one of the first predetermined reflection surface 8 and the second predetermined reflection surface 10 used in step a.

5 It also follows for TRIWEX that it holds, when used in the embodiment according to figures la, lb, 2a, 2b, and wherein the object is a plate or pipe as discussed that the second outer wall 10 forms the at least one predetermined reflection surface used in step a., the first outer wall 8 forms the first predetermined reflection surface used in step b. and the second outer wall 10 10 forms the second predetermined reflection surface used in step b (this is the situation in figure 10a); or the second outer wall 10 forms the first predetermined reflection surface used in step a, the first outer wall 8 forms the second predetermined reflection surface used in step a. and the second outer wall 10 forms the at least one 15 predetermined reflection surface used in step b.(this is the situation in figure 10b).

More particularly it holds in that case that in step a. only the second outer wall 10 is used as the at least one predetermined reflection surface and that in step b. the first outer wall 8 is used as the first predetermined 20 reflection surface and the second outer wall 10 is used as the second predetermined reflection surface (this is the situation in figure 10a); or that in step b. only the second outer wall 10 is used as the at least one predetermined reflection surface and that in step a. the first outer wall 8 is used as the second predetermined reflection surface and the second outer wall 10 is used as the 25 first predetermined reflection surface (this is the situation in figure 10b).

Time-space versus frequency-wavevector domains

Implementation of step c. for IWEX, SKIWEX, TIWEX and TRIWEX as 30 well as other examples according to the invention can be in the space/time (x / 29 t) domain, the space/frequency (x / w) domain, the wave-number/frequency domain (/¾ / w), or the wave-number/time domain (k / t).

The main advantage of the space-time domain is that it can be interpreted quite intuitively.

5 The space-frequency domain is less intuitive, but allows for more efficient implementation in the Matlab environment used in the work described in this application. The IWEX algorithm (step c for IWEX) is a convolution operation in time, which translates to a multiplication in the frequency domain. Matlab can multiply matrices very efficiently. Both the 10 IWEX dataset and the frequency domain back-propagation kernels can be represented as matrices. This was the main reason to implement IWEX in the space/frequency domain. The Kernels describe the propagation of wave fields created by a line source and a factor from a Rayleigh integral, this is known from the reference to Gisolf & Verschuur (The principles of Quantitative 15 Acoustical Imaging, by Dries Gisolf and Eric Verschuur; ISBN 978-90-73781-93-1) and older publications.

As mentioned above, SKIWEX, TRIWEX and TIWEX rely on waves reflected by the at least one predetermined reflection surface (also referred to in this application as an outer wall of a plate or pipe or as an outside wall or 20 inside wall of a pipe) twice, or once, respectively, to image the object under inspection. Because of this, it looked as if the reflection coefficient of the predetermined reflection surface wall should be taken into account when processing the datasets. The reflection coefficient depends on the angle of the plane incident wave. Implementation of predetermined reflection surface 25 reflection coefficient correction can, therefore, only be carried out in the wave-number/frequency domain. This domain is even less intuitive than the space/frequency domain, but the implementation of the angle-dependent reflection coefficient boils down to a multiplication in the SKIWEX algorithm (using the slowness as the input parameter to compute the reflection 30 coefficient). It turns out, however, that the reflection coefficient is nearly 30 constant over the relevant range and does not need to be taken into account.

See below for more details.

Possible derivation of an IWEX over skip algorithm (SKIWEX, TIWEX, TRIWEX and others) 5

Name algorithm IWEX over skip / SKIWEX / TIWEX/ TRIWEX Objective Image a weld with a cap

Approach Use over skip information to image the region of interest and defects with illumination from below (SKIWEX) and from the side (TIWEX, TRIWEX).

Advantages - Removal of the blind area near the front wall - Imaging of the Tar side’ of the defect (i.e. from below) - Imaging with a gap in the aperture is possible

Drawbacks - Imaging accuracy depends on the back wall geometry

Critical - Wall thickness parameters

Notes

There is another reason why back-propagation kernels are preferably calculated in the wave-number/frequency domain, although they are actually applied in the space/frequency domain. In the wave-number/frequency domain 10 a simple filter can be designed to remove aliasing in the kernel due to insufficient spatial sampling of the wavefields, i.e. the pitch of the transducers is too coarse according to the Nyquist sampling criterion;

Ar =-^- (1) 2/maxSin<5 where vmm is the minimum propagation velocity in the system (usually the shear velocity vs), /max is the maximum frequency in the spectrum and <5 is the 15 31 maximum angle under which waves depart from the sources, or arrive at the receivers. After filtering of the kernels in the wave-number/frequency domain to remove abasing effects, the kernels are transformed back to the space/frequency domain for apphcation to the data. Even without filtering the 5 kernels, the fact that they are calculated in the frequency/wave number domain already handles the aliasing in a way that leads to smaller artefacts than when they are directly calculated in the space/frequency domain.

The original reason for calculating the kernels in the wave-number/frequency domain, the inclusion of a correction factor for the reflection 10 coefficient of the back wall, has never shown observable effects and is, therefore, not apphed, but the kernel alias protection can be relevant, depending on the application.

The main objective of the IWEX over skip algorithms (in this document also referred to as examples SKIWEX, TRIWEX and TIWEX) is to create an 15 image by using the back wall as a mirror (see figures 11a and lib). For example, point D in the figure can be imaged directly by IWEX and indirectly by the SKIWEX, TIWEX and TRIWEX algorithms. The IWEX algorithm was originally designed to use compression waves for imaging. Also the SKIWEX algorithm is designed to use compression waves for imaging. However, both 20 algorithms can easily be adapted to use shear waves, as is demonstrated below. The TIWEX and TRIWEX algorithms are designed for imaging with shear waves. However, TIWEX and TRIWEX can also be adapted to use compression waves.

Alternative methods that use different wave modes and/or speed of 25 sound for the various parts of travel respectively are also considered part of the invention. Basically this means that in the calculation according to the invention for different parts of the path of travel of ultrasound within the object different speeds of ultrasound are used. For each such part calculations can be made according to the principle of inverse wave field extrapolation on 30 the basis of the speed of ultrasound within such part. For instance mode 32 conversion at any reflection surface (of the object or defect) like for Round Trip Tandem, may be used and, although not described here in detail, are considered part of this invention. As is generally known after mode conversion the speed of the ultrasound differs from the speed of the ultrasound before its 5 mode was converted.

The use of a wedge (a possible example)

The plurality of transmitters T and the plurality of receivers R may be 10 combined in a plurality of transducers (16i, 16i.j.) which may be combined in a probe wherein each transducer can transmit and receive. This is one possible means for carrying out the method according to the invention. The transducers may be mounted on a plastic (e.g. Perspex) wedge with a wedge angle specifically calculated to exceed the critical angle corresponding to compression 15 waves in steel to ensure that mainly shear waves enter the steel plate, which give higher resolution images than compression waves due to their lower velocity (fig. 12).

Fig 12 shows an example of a ray path for TIWEX (with coinciding source and receiver). The angle y has been designed so that for all potential defect 20 locations in the weld area the angle a exceeds the critical angle for P to P refraction at the wedge-steel interface. Consequently the target area is only illuminated by S-waves.

If a wedge is used the (this is preferred but not necessarily required) first algorithmic step in step c. to be taken, be it for IWEX, SKIWEX, TRIWEX 25 or TIWEX, is to back-project sources and receivers through the wedge, to equidistantly sampled locations of virtual sources and virtual receivers along the front wall 8. The geometry and the coordinate systems are shown in figure 13 and these coordinates are used in the below formulas (2) - (4). The transducers, acting in this example as both sources and receivers, are 30 positioned along the dot-dash fine. Since this is considered a 2D problem, the 33 sources and receivers are supposed to have a line-source and line-receiver character, respectively. For a transducer-array with a pitch of .425 mm and a width of 15 mm this condition seems well satisfied.

Through the use of a double back-propagating Rayleigh integral we can 5 now calculate the recording of a virtual source/receiver pair located in positions A' and A respectively (formula 5.9 in Gisolf & Verschuur): P^a„Ca.^a,Qa) = Qa,Qa——\ J d^sd^RP(^s,0;tR,0) —--(2)

ZniVp p p 10 where vp is the P-wave velocity of the plastic wedge and where: p = V(^-^)2+ci ’ p' = V(^-^')2 + ci' (3) and: 15 G=f-^-^]tany , £A. = f—— “litany (4) ^cosy J l^cosy

The first group of arguments in P gives the source coordinates, the second group of arguments gives the receiver coordinates. P represents the transmitted ultrasound signal (thus the transmitted ultrasound wave field), in 20 this case in the form of a pressure wave.

There has been now created a new data acquisition level with length Lw along the front wall of the steel plate. This process is also called redatuming.

In the new coordinate system (x, z) for the redatumed dataset we write: 25 P(xA„0;xA,0) = P^A„CA^A,CA) (5) with: V, = ^ cosysin y , xA, = %A, cosy -QA,siny (6)

At the front wall 8 there is transmission from longitudinal (pressure) to longitudinal and transmission/conversion from longitudinal to transversal (shear), for waves passing the interface from above. Similarly, there is 30 34 transmission and transmission/conversion for the waves passing the interface from below. For incident pressure -waves from above, the transmission coefficients are shown in figure 14. Figure 14 shows the transmission coefficients Tpp and Tps (real and imaginary part) for a plastic/steel interface.

5 Note that in the range of angles of incidence between 30° and 60° there is little transmission of pressure-waves and a fairly constant angle-in depen dent conversion of pressure waves to shear waves.

Note that in the relevant range of angles of incidence in the plastic wedge (appr. 30° to 60°, given a wedge angle y of 33°) the transmission 10 coefficient Tpp is small and the transmission/conversion coefficient Tps is virtually angle-independent. For this reason all energy entering the steel plate is considered to be shear and the actual transmission/conversion coefficient is considered constant and is not taken into account.

15 Aliasing of the hack-propagation kernel (a possible example)

In formula (2) the data is aliased if the pitch is not strictly satisfying the sampling criterion given by formula (1). For example, in a plastic wedge with dp = 2860 m/s and for a maximum frequency of 7 MHz , a pitch of .425 mm will 20 only allow a maximum departure, or arrival angle of 29°, to avoid aliasing.

This fits nicely with the directivity pattern of the transducers, which is of the same order of magnitude.

However, in formula (2) there is not only the data, but there are also the back-propagation kernels. In their theoretical form, as shown in formula (2), 25 they would imply a maximum angle of arrival or departure of 90°, which will introduce aliasing in the result of back-propagation, due to the .425 mm pitch, even if the data itself is contained within the 0 - 30° angle range.

Fig. 15 shows left: back-propagation kernel in k / / domain (k-range is from 0 to 2 kNyquist). Note the discontinuity around kNyquist. Middle: full cosine square 35 tapered k / ƒ filter. Right: back-propagation kernel after k / f filtering. Note that the discontinuity around kNyquist has been removed.

The abasing issue of back-propagation kernels is illustrated in figure 15. On the left we see a kernel for back-propagation through plastic from a data 5 acquisition plane with pitch .425 mm., to an arbitrary location along the front wall. The kernel is calculated directly in the k / f domain. According to the strict criterion of formula (1), with Vmin = 2860 m/s and fmax = 7 MHz, the Nyquist wavenumber should be 2450 nr1, as opposed to 1180 nr1 from the .425 mm pitch. Building up the kernel in the k If domain avoids the abasing, but 10 creates a strong discontinuity at the Nyquist wavenumber. Appbcation of the k / ƒ filter shown in the middle figure in figure 15 removes the discontinuity. Subsequently the filtered kernel is transformed to the space/frequency domain for appbcation. In some applications the data itself may act as such a filter and no additional filtering is then required, provided the kernel is calculated 15 in the k / / domain, as shown in figure 15.

The back-propagation kernels for imaging (a possible example for step c.) 20 Imaging of the transmitter and receiver data at the front wall 8 (this may be virtual source and virtual receiver data at the front wall 8 if a wedge is used), to any image point D (=first predetermined position) in the object domain, involves a back-propagation step of sources (transmitters) and receivers. In any point D in the image domain, the grey shaded area in figure 25 16 a, virtual coinciding source/receiver pair is created with the help of a

Rayleigh integral similar to formula (2).

Depending on the imaging mode appbed (IWEX, TIWEX, SKIWEX TRIWEX or other), we choose a combination of back-propagation kernels connecting the source and receivers along the front wah to the image point, 30 with, or without a reflection at the back wall. The combination of the sobd 36 path (60) and solid path (62) in figure 16 will give IWEX imaging. In figure 16 the object to be inspected extends from z=0 to z=zb The combination of the dot-dash path (64) and the dot-dash path (66) will give us SKIWEX, whereas both the combinations sohd path (60) with dot-dash path(66) and solid path (62) 5 with dot-dash path (64), will give us TIWEX. The combination of dot-dash path (64) with the dotted path (68) will give TRIWEX. Figure 16 shows the six different back-propagation trajectories from sources and receivers, with and without back wall 10/ front wall 8 skips. Please note that the back wall forms thus a predetermined reflection surface for TIWEX, SKIWEX and TRIWEX.

10 Front wall 8 also forms a predetermined reflection surface for TRIWEX. The shaded area is the image domain, in which every point on a fine grid with a grid-spacing for example equalhng half the element pitch, in turn, becomes the image point D. For IWEX and SKIWEX also elements at the other side of the weld-cap can be used.

15 Like in formula (2), the back-propagation kernel from the source or receiver locations along the front wall, to an image point D in the image space, is given by: ~ id) p jvs -- ’ p = \I(x~xd)2 + 4 (7) 20 where vs is the S-wave velocity of the ultrasound within the object shown in figure 16. Transferring the receiver R back to point D by means of formula (7) is referred to as inverse wave field extrapolation. Basically the transferring of 25 the source to point D involves a forward field extrapolation. However, due to the principle of reciprocity, sources and receivers can be interchanged. The forward wave field extrapolation from a transmitter T to a point D is thus equivalent to an inverse wave field extrapolation from point D to transmitter T, enabling the use of the same formula (7) for both parts of the propagation 30 path.

37

Similarly, for the back-propagation kernel of the source or the transmitter to the virtual image point D including a back-wall skip, it holds: K5(xD,zD,x,Q) = (2zb - zA) —-—-—-— , ps = ^(x-xD )2 +{2zb - zDf (8) \2mvs pj 5

Similarly, for the back-propagation kernel of the source or the transmitter to the virtual image point D including a back-wall skip and a front wall skip, one obtains: j a, ejV* j-j-y KJx2,zD,x,0) = (2z£+zA) —--, p„=^j(x-xD) +(2 zB + zD) V Pss (g) 10

Thus the above formulas are used in step c.

Formula (7) is used for the inverse wave field extrapolation from source T or receiver R to point D (predetermined position).

15 Formula (8) is also used for the inverse wave field extrapolation from source T or receiver R to point D (predetermined position). It takes however into account that in step a. or step b. the back wall functions as a predetermined reflection surface.

Formula (9) is also used for the inverse wave field extrapolation from 20 source T or receiver R to point D (predetermined position). It takes however into account that in step a. or step b. the back wall and the front wall each function as a predetermined reflection surface.

In step c. for IWEX the formula (7) is used twice (for taking into account in the inverse wave field extrapolation that neither in step a. nor in step b. a 25 reflection on the back wall takes place).

In step c. for SKIWEX formula (8) is used twice taking into account in the inverse wave field extrapolation that the back wall functions as a predetermined reflection surface both in step a. as well as in step b.

In step c. for TIWEX formula (7) is used once for taking into account in 30 the inverse wave field extrapolation that either in step a. or in step b. no 38 reflection on the back wall or front wall takes place. Furthermore in step c. for TIWEX formula (8) is used once for taking into account in the inverse wave field extrapolation that the back wall functions as a predetermined reflection either in step a. or in step b.

5 In step c. for TRIWEX formula (8) is used once for taking into account in the inverse wave field extrapolation that the back wall functions as a predetermined reflection either in step a. or in step b.. Furthermore in step c. for TRIWEX formula (9) is used once for taking into account in the inverse wave field extrapolation that the back wall and the front wall both function as 10 a predetermined reflection surface either in step a, or in step b.

As mentioned before, it is preferred to calculate these kernels in the horizontal wave-number/frequency (kx / to) domain and subsequently numerically transform them back to the space/frequency (x / to) domain.

Analytic transformation of formulas (7) and (8) to the kx domain is 15 defined as follows: K (xD,z0;&x) = j dx elk*x K (xD,zD;x,0) (10)

-CO

Transformation of formulas (7), (8) and (9) according to formula (10) is readily carried out with the help of the stationary phase method (formula 6.18 in Gisolf & Verschuur). The resulting kernels in the kx domain are; 20

(ID

K\xD,z^,kI) = eK

with: 25 (12) 39

After calculation of the three kernels (the three formulas (11)) with the help of formulas (11) and (12), for all image points D in the entire object domain, the kernels are numerically transformed back to the (x/ a) domain.

They can now be applied to the redatumed dataat the front wall, thus 5 applied to the calculated virtual source and virtual receiver data as indicated in formula (5).

For application of the IWEX algorithm it than holds: P(XD’ ^£>3 xD, z D) — QdxRdxsK [xD, zD, xr,Ó^K (^xd,zd,xr,0}P(^xs, 0, xR, (13) 10

For SKIWEX it than holds: P[xd’zd’xd’zd) ~\\^xi\dxsKs(v/,,z/,,x/(,0(xD,zD,xs,0jP(xs,0,xR,0) (14) 15 For TIWEX it than holds: P{XD’ ZD’XD’ zd ) — JJ dxRdxsKs (xd,zd,xr,0^K [xd,zd,xs,0^P(xs,0,xr,0^ (15) whereas for TRIWEX it than holds: 20 P{xD,zD,xD,zD) = \\dXjdxsK5 (xD,zD\xk,0)KJxd,zd-, xs,0) P(xs, 0; xR,0) (16)

In the formulas 13-16 p represents the measured data (=receiving 25 signal) obtained by one receiver of the group comprising a plurality of receivers if one transmitter transmitted.

Thus each formula calculates for one predetermined position and for one combination of one receiver and one transmitter the transferred P and repeats 40 this for each possible combination of one transmitter and one receiver wherein the calculated results for each such possible combination are summed. This summing is indicated by the double integral over all transmitter and receivers. In fact this therefore stands for a summation over all transmitters and 5 receivers.

P stands for the wave field (= the signal which would be received) at one predetermined position within the object.

As already explained the formulas (13)-(16) indicate the path of the receiver to the predetermined position and the path of the transmitter to the 10 predetermined position. Basically the virtual source and the virtual receiver are both transferred to the position D by means of the formulas. The signal which would be received by the virtual receiver and which would originate from the virtual transmitter while reaching the virtual receiver via the path which includes the predetermined position corresponds thus in formulas (13)-15 (16) with the received signal having a travel time equal to zero (because both the virtual transmitter and the virtual receiver are calculated to be transferred to the predetermined position.

Note that for TIWEX and TRIWEX, the indices of source and receiver positions in the kernels can be interchanged (swapped). Because of 20 source/receiver reciprocity in the data, it should not matter which of the two kernels used in each of the formulas (13)-(16) is applied to the sources, or to the receivers. However, if the data is not reciprocal in the sources and receivers, possibly due to external noise, or different directivity patterns for transmission and detection, it may be advantageous to apply formulas (15) and 25 (16) twice, once with the single skip in the receiver path and once with the single skip in the source path, and average the results.

Based on the above formulas (13)-(16) IWEX, SKIWEX, TIWEX and TRIWEX can be carried out if a wedge is used.

If no wedge is used the same formulas (13)-(16) apply wherein however 41 p (xs, o; xr, 0) is replaced by P(xs, o, xr, 0) wherein P(xs, o, xr, 0) is the transmitted ultrasound signal by the transmitter/source which is positioned directly on the surface of the object.

Based on the above formulas (13)-(16), if a wedge is used, or the 5 amended formulas as discussed above if the transmitters (16.i, 16.i.j, T) directly transmit the ultrasound signal into the object (1, 2, 4), method step c. can be carried out. The formulas provide the method steps for the inverse wave field extrapolation as explained by means of figures la-6. More particularly the formulas enable to mathematically reverse the time, on the basis of the 10 receiving signals. The time reversal is already contained in the kernels and does not need to be applied to the data. With these formulas, the detected wave field is traced back to the position where it came from, namely the position of the virtual sources. In this example, these virtual sources may, for instance, be welding defects. The wave theory takes into account both the amplitude and 15 the delay time of the signal as well as the possible reflection of the transmitted signal on the at least one predetermined reflection surface (8, 10).

For figure 5 it was explained: first, source and receive elements are chosen. In this example, elements 50 and 59 have been selected as transmitter and receiver, respectively. Then, an image point in the volume is chosen; for 20 instance point A, which is positioned on a location without defect. In the dataset, the time trace corresponding to transmitter 50 and receiver 59 is selected. After correction for amphtude and phase differences (using the Rayleigh integral), the amplitude corresponding to time of flight tTAR is stored in a temporary matrix, at coordinates (xa, za). As there is no defect in point A, 25 the amplitude Atar is low; and hence a small value is stored in the image matrix. Basically tTAR can now be calculated on the basis of the formulas (13)- (16) if a wedge is used or the amended formulas as discussed above if the transmitters (16, T) directly transmit the ultrasound signal into the object.

The same calculation is carried out for the other transmitter/receiver 42 combination and all the calculation results are summed and stored in the matrix.

Therefore the formulas (13)-(16) describe a summation of the receiving signals for all transmitter/receiver combinations transferred back to the 5 predetermined position. This summation can be regarded as an image at the predetermined position. For each such predetermined position within the predetermined area the corresponding ultrasound signal at that location can now be calculated. All these calculations per predetermined position in combination provide an image of the area 28 to be investigated.

10 In view of the above it may hold according to the invention that step c.

comprises calculating for the predetermined position within a predetermined area, and based on the receiving signals obtained in step b., ultrasound signals at this position (the sum of all such signals is indicated as P in formulas (13)-(16) which would provide the receiving signals obtained in step b. respectively, 15 wherein said calculation is based on the principle of inverse wave field extrapolation, wherein the method further comprises repeating step c. for a plurality of different predetermined positions within the predetermined area to obtain information for building up an image of the predetermined area.

If step a. is repeated for another ultrasound transmitter from the first group of 20 ultrasound transmitters wherein step b. is repeated using a plurality of ultrasound receivers from the group of ultrasound receivers for each repeated step a. and wherein step c. is carried out for each repeated step b, then the result as discussed for formulas (13)-(16) is obtained which formulas also include the summation of other transmitter/receiver pairs for other 25 transmitters.

Also in view of the above it will now be clear that in step c for each receiving signal obtained in step b., one of said calculated ultrasound signals may be calculated based on the principle of inverse wave field extrapolation.

Also in view of the above it will now be clear that in step c. for each receiving 30 signal obtained in step b., said calculated ultrasound signal is preferably 43 calculated for a moment in time that the calculated ultrasound signal forms a response to the transmitted ultrasound signal in step a.

Also in view of the above it will now be clear that in case a wedge is used, step c. may comprise to calculate first the travel of the transmitted 5 ultrasound signal through the wedge using the principle of forward wave field extrapolation and subsequently to calculate the continued travel of the transmitted ultrasound signal through the object using the principle of forward wave field extrapolation and wherein step c. may comprise to calculate first the travel of the ultrasound signals through the wedge using the principle 10 of inverse wave field extrapolation and subsequently to calculate the preceding travel of the ultrasound signals through the object using the principle of inverse wave field extrapolation if in step b. the ultrasound signals are received through the wedge.

Thus the image point may be represented as discussed for figure 5 15 within the image by a pixel having a color and/or intensity which corresponds with the sum of the calculated values of the plurality of ultrasound signals calculated in steps c. for the predetermined position. The calculated ultrasound signal may be represented by a complex number comprising the amplitude and phase of the calculated ultrasound signal on said moment in time.

20

The imaging condition

In formulas (13)-(16), the signal recorded by a virtual receiver in point D, of a wave field generated by a virtual source in the same point D can be 25 calculated. The image amplitude in D is now extracted from this signal by application of the imaging condition (Gisolf & Verschuur, Section 5.2).

In its simplest form, the imaging condition means selecting the sample value from the coinciding source and receiver signal, corresponding to the travel time from source to receiver. For coinciding source/receiver this travel 44 time is obviously zero, meaning that the first sample in the time domain representation of the signal is selected.

Alternatively, we can integrate the frequency domain representation of the signal over all frequencies.

5 The resulting value (from any of the above possible methods (there are more possible imaging conditions) is assigned as image amplitude to the coordinates of the point D. The full image is created by covering the whole image space with image points D, which in turn become coinciding virtual sources and receivers. The image points are discretized on a grid covering the 10 object space indicated in figure 16. Usually the grid spacing is chosen equal to half the element pitch.

The above means for the simplest form that, in step c. based on the receiving signals obtained in step b., new corresponding receiving signals are calculated wherein the new corresponding receiving signals are now an 15 assumed result of a virtual receiver and virtual transmitter being present at the predetermined position wherein from the calculated new corresponding receiving signals, characteristics are selected which correspond with an assumed travel time from the virtual source to the virtual receiver being equal to zero.

20 Alternatively this means that, in step c., based on the receiving signals obtained in step b., new corresponding receiving signals are calculated wherein the new corresponding receiving signals are now an assumed result of a virtual receiver and virtual transmitter being present at the predetermined position wherein the new corresponding receiving signal is integrated over all 25 frequencies in the frequency domain representation of the new corresponding receiving signal for obtaining the calculated ultrasound signal for a moment in time that the calculated ultrasound signal is a response to the transmitted ultrasound signal in step a.

Wave shape and phase in the image domain 30 45

Ideally, for a delta-pulse source wavelet, we would obtain an image with non-zero amplitudes at the positions where the wave field was scattered, and zero amplitudes everywhere else. However, due to the finite length of the band-limited pulse that is used, we do find the pulse shape back in the image, 5 as an expression of the band-limitation in the method. In addition, the pulse shape in the image domain may appear stretched, due to obhque illumination of the defect (Gisolf & Verschuur, Section 5.3). It is expected to see an undistorted pulse shape in the direction of normal incidence illumination.

If in the pre-processing of the data, the minimum phase pulse that was 10 used in the field is converted to a zero-phase pulse, we expect to see maximum amplitude at the position of the defect, with sidelobes perpendicular to the direction of normal incidence illumination, assuming that in the imaging process the zero-phase character of the data is maintained.

With the double back-propagation integrals in formulas (13)-(16) there 15 is still an issue regarding the phase of the resulting signal with coinciding virtual source and virtual receiver. The first back-propagation is fine, because we stay away from the mirror source location for the image point location. However, in the second back-propagation step we actually image a secondary point-source. For image point location beyond the secondary source in a 20 scattering point we violate the condition that there should be no sources in the interval over which we back-propagate. The second back-propagation step should be interpreted as summing over all the individual images from the original sources. There should be no phase correction involved, but the data should be scaled to avoid over emphasis on the longer offsets. To keep the 25 source and receiver kernels symmetric, what is currently implemented in TIWEX is a Jïfm correction to each of the kernels in formula (15), which gives excellent results, see figure 17.

Figure 17 shows a synthetic example of three point defects along the bevel 100 of a weld 6, illuminated in TIWEX mode with shear waves (see 46 figure 16). The illuminating pulse was zero-phase. Note that a zero-phase image is obtained in the direction perpendicular to the illumination.

In Figure 17 the band-limited character of the imaging is illustrated. The synthetic data is acquired with the help of a wedge (see figure 12) with a 5 wedge angle of 33°. The responses of three point diffractors are modeled, as shown in figure 17, and the data is imaged by redatuming the data from the top of the wedge to the front wall, as compression waves, and subsequently imaging the object domain from the redatumed data-set, as shear waves, in TIWEX mode. As can be appreciated from figure 12, the illumination is 10 predominantly from the side and it is indeed in this direction that we find the undistorted zero-phase pulse shape, with amplitudes peaking at the defect locations.

The stretch effect due to oblique illumination that was mentioned above, is limited by application of an illumination mask to the redatumed data, which 15 only allows traces to be used in the imaging for which the illumination angle (angle between incident and scattered rays) for all image point locations is less than 100°. The working of this illumination mask is explained below.

The reflection coefficient of the back wall (TIWEX, SKIWEX, TRIWEX) 20

In TIWEX, TRIWEX and SKIWEX, one and two back wall reflections respectively, are used for the imaging process. It was already mentioned that the shear to shear reflection coefficient of the back wall (10) reflections does not need to be taken into account. In this section we will illustrate this. In 25 figure 18 the reflection coefficient shear to shear for a steel/air interface is shown. The critical angle is the angle of incidence for which the converted compression wave propagates horizontally. Note that in the likely range of angles-of-incidence between 30° and 60°, the shear to shear reflection coefficient is virtually constant and equal to one.

47

In figure 18 it is shown that the real and imaginary part of the shear to shear reflection coefficient for a steel to air interface. The critical angle that is visible in the figure is the angle where the shear to compression converted wave propagates horizontally. It can easily be seen that for small bevel angles 5 and a maximum angle-of-incidence of 50° for specular reflections along the bevel, the angle-of-incidence at the back wall (10) will never be less than 30°.

In this angle range the reflection coefficient Rss at the back wall is constant and equal to one. This is the justification for ignoring the back wall reflection coefficient in the imaging. The same applies to the top wall (8) which is also 10 used for TRIWEX. As a result, some calculations can be simplified, e.g. by using ray tracing for the kernels, without significantly affecting the quality of the resulting images.

The illumination mask (TIWEX) 15

As mentioned before, illumination with a large angle between incident and scattered rays gives a stretched image. To avoid this, we limit the number of source/receiver combinations that illuminate a certain image point A to 20 those with an illumination angle 3 < 100° (see figure 19). Figure 19 shows a TIWEX geometry for given source position, receiver position and image point location A (= predetermined position). For every image point A in the object domain a source/receiver mask can be calculated to blank all data traces for which the illumination angle 3 exceeds 100°. This is to limit stretch effects 25 due to oblique illumination.

The relationship between xs, xr and 3 is calculated for every level za , in the most unfavorable location where xa-Ld . In the configuration shown in figure 19 we have: 30 3 = n-cpR-(ps (17) or: 48 tan 9 = tan<pfi + tan <ps (18) 1 - tan<pR tan q>s

With: tan cp s =xs-L° and tan cpR = xz~L° (19)

Z A ^ Z b — Z A

5 it holds: tanS = (2zB ~za)(xs -LD)+zA(xR -Ld) (20) (½ - Ld )(½ - Ln)~ za(2zb - za)

Because of reciprocity it is desired to make this symmetrical in xs and xr : tan3 =_z* (ss + xR -2Ld)_ (21) (½ - Ld)(XR -Ld)- ZA (2zb - ZA ) 10

The condition S < Qmux (Smax > % n) then translates to: tan 5 < tanSmax | (xs - LD)(xR - L D) > z A(2z B - z A) (22) 15 When this condition is fulfilled the data trace (xs, xr) is accepted for imaging at depth za , otherwise it is rejected. The difference between applying an illumination mask and not applying one is shown in figure 20. From formula (22) it is clear that the effect of the illumination mask increases with depth.

The broadening of the main lobe and the widening of the ‘smiles’ due to stretch 20 are clearly visible in figure 20. Figure 20 shows left an imaging of the synthetic data-set of figure 17 with the illumination mask limiting the maximum illumination angle to 100°. Figure 20 shows right an image of the same dataset without application of an illumination mask. Note the stretch in the pulse shape due to oblique illumination.

25 The invention is not limited to the provided examples. This applies both to the hardware as to the used algorithm in the hardware and method. The system as shown in figures la, lb may, according to the invention, comprise 49 control means 22 for carrying our step c. These control means may also be arranged for carrying out step a. and/or step b. in conjunction with the transmitters and the receivers. Also step c. may be carried out by means of a computer separate from the control means 22.

5 For the sake of completeness, it is again remarked that this technology can be used for all kinds of objects such as metal plates and pipes. Such a pipe 70 is shown in figure 21. It comprises an outside wall 72 and an inside wall 74. The technologies described for figures 7-20 can be applied to the pipe wherein for 10 example the outside wall 72 corresponds to the front wall 8 and the inside wall 74 correspond to the back wall 10.

Also, as is shown in figure 22a, for a used combination of a transmitter T and a receiver R the transmitter may he on the front wall 8 and the receiver may lie on the back wall 10 of for example a plate. In this example both the 15 front wall as well as the back wall function as a predetermined reflection surface. The kernels Ks for a skip on the back wall can be used in step c. and a similar Kernel for a skip on the front wall can be calculated and used in step c. along the fines as discussed above.

Also, as is shown in figure 22b, for a used combination of a transmitter T 20 and a receiver R the transmitter may fie on the back wall 10 and the receiver may fie on the front wall 8. In this example both the front wall as well as the back wall function as a predetermined reflection surface. The kernels Ks for a skip (reflection on predetermined reflection surface) on the back wall can be used in step c. and a similar kernel for a skip on the front wall can be 25 calculated and used in step c. along the fines as discussed above.

Also, as is shown in figure 23a, for a used combination of a transmitter T and a receiver R the transmitter T may fie on the front wall 8/outside wall 72 of a pipe 70 and the receiver may fie on the back wall 10/inside wall 74 of the pipe. In this example both the front wall as well as the back wall function as a 30 predetermined reflection surface. The kernels Ks for a skip on the back wall 50 can be used in step c. and a similar kernel for a skip on the front wall can be calculated and used in step c. along the lines as discussed above.

Also, as is shown in figure 23b, for a used combination of a transmitter T and a receiver R the transmitter may lie on the back wall 10/inside wall 74 of 5 the pipe 70 and the receiver may lie on the front wall 8/outside wall 72 of the pipe 70. In this example both the front wall as well as the back wall function as a predetermined reflection surface. The kernels Ks for a skip (reflection on predetermined reflection surface) on the back wall can be used in step c. and a similar kernel for a skip on the front wall can be calculated and used in step c. 10 along the lines as discussed above. Of course, in the example of figures 21-23, a plurality of transmitters and a plurality of receivers can be used for providing a plurality of mutually different combinations of a transmitter and a receiver. Each combination is used for transmitting and receiving and all receiving signals can be processed in step c. as explained above.

15 Furthermore it will now be clear that the path from the transmitter to the predetermined position may reflect a plurality of times along a plurality of predetermined reflection surfaces. These reflection surfaces need not to be parallel or flat. The only thing that is required is that the position and angle of reflections as such are known so that the correct kernels can be calculated. It 20 will also be clear that the path from the receiver to the predetermined position may reflect a plurality of times along a plurality of predetermined reflection surfaces. These reflection surfaces need not to be parallel or flat. The only thing that is required is that the position and angle of reflections as such are known so that the correct kernels can be calculated. This would hold for each 25 transmitter-receiver combination/pair which is used. It may even be that for different pairs/combinations of transmitter/receiver different sets of predetermined reflection surfaces are used. Then for each pair the specific kernels can be calculated and for each pair the received signal can be calculated back to the predetermined position as explained above.

30 Subsequently these calculated results per pair can be summed to obtain an 51 image point for the predetermined position. It may even be that for different predetermined positions different reflections surfaces for the same pairs/combinations of transmitter/receiver are used. This will all depend on the geometry of the object and the positions of the transmitters and the receivers.

5 Furthermore for each receiver a wedge may or may not be used. Also for each transmitter a wedge may or may not be used. There may be used a fluid between the transmitter and the object for acoustically coupling the transmitter and the object. There may be used a fluid between the receiver and the object for acoustically coupling the receiver and the object. A 10 transmitter and a receiver may be combined in a single transducer. These transducers may be arranged in a one or two dimensional array. A plurality of transducers may be combined in a probe. Different probes may be used, for example in the case of figures 22 and 23 wherein at least one probe may be positioned on the front wall and at least one probe may be positioned on the 15 back wall. It may however also be that the individual transmitters and receivers are used. It may be that a plurality of transmitters are arranged in a one- or two-dimensional array and may be combined in a transmitter probe. It may be that a plurality of receivers are arranged in a one- or two-dimensional array and may be combined in a receiver probe. It may be that the 20 predetermined group of transmitters comprises only one transmitter. In that case still different transmitter/receiver combinations/pairs can be obtained because the predetermined group of receivers comprised a plurality of receivers. If there is a plurality of transmitters it may be that they transmit at the same time and in fact are used as an equivalent to one transmitter. In that 25 case again different combinations of transmitter and receivers are obtained because there is a plurality of receivers. If there is a plurality of transmitters and a plurality of receivers it is efficient that the transmitters transmit a different moments in time. For each transmitter of the predetermined group of transmitters which transmits, all receivers are used at the same moment in 30 time for receiving a plurality of receiving signals corresponding with the 52 plurality of receivers which receive at the same time. This has been explained on the basis of figures 4-6.

It is further remarked that in an example the approach in step c. is using forward extrapolation (from the transmitter to point D) and inverse 5 extrapolation (from the receiver to point D) by means of the kernels. In this implementation in the algorithm the first path from transmitter to D and the second path from receiver to D are calculated. Then the measured ultrasound signal for the mentioned transmitter-receiver pair/combination is time-shifted to tO according to the duration along the first path and the second path. This 10 has been explained on the basis of formulas 13-16. However, alternatively the measured signal (=receiving signal) is evaluated at the time corresponding to the travel time along the first path and the second path. All approaches are valid and lead to the same result. As explained above the method according to the invention is suitable for investigating an area below a weld cap even 15 though the transmitters and the receivers which are used in the method according to the invention cannot be positioned on the weld cap for transmitting ultrasound in the object and receiving ultrasound from the object. Instead the transmitters and receivers can be positioned on a different part of the outer surface of the object. Similarly the method can be used to investigate 20 an area below an uneven surface of the object even though the transmitters and the receivers which are used in the method according to the invention cannot be positioned on the uneven surface for transmitting ultrasound in the object and receiving ultrasound from the object. Instead the transmitters and receivers can be positioned on a different part of the outer surface of the object. 25 Similarly the method can be used to investigate an area below a portion of the surface of the object even though the transmitters and the receivers which are used in the method according to the invention cannot be positioned on that portion of the surface for transmitting ultrasound in the object and receiving ultrasound form the object because this portion of the surface is not accessible 30 (it may not be accessible because of another object which is close to this part of 53 the surface). Instead the transmitters and receivers can be positioned on a different part of the outer surface of the object which is accessible for the transmitters and receivers.

Claims

A method for examining the internal material of an article (2, 4, 6) from an outer surface (8) of an article using ultrasound e.g. with a frequency of at least 100 kHz, the method comprising the steps of : A. Transmitting at least a first ultrasound signal from an at least first ultrasound transmitter of a predetermined group of ultrasound transmitters to the internal material of the object (2, 4, 6) where in the internal material of the object reflections and / or diffractions of the first ultrasound signal take place, 10 b. receiving reflections and / or diffractions of the first signal from the internal material of the object using a plurality of ultrasound receivers from a predetermined group of ultrasound receivers (16.i) which multiple of ultrasound receivers are acoustically coupled to the outer surface (8) of the object at positions spread over at least one dimension of the outer surface of the object, with each of the plurality of ultrasound receivers (16.i) generating a reception signal of the received reflections and / or diffractions of the at least first ultrasound signal of the internal material of the object, c. in combination processes the receiving signals generated by the plurality of ultrasound receivers to determine, according to the principle of inverse wave field extrapolation, where in the interior material of the object reflections and / or diffractions of the transmitted first ultrasound signal take place; characterized in that, the object is provided with at least one predetermined reflection surface wherein in step a. the first ultrasound signal is transmitted such that it reflects at least once within the object on the at least one predetermined reflection surface before it has a first predetermined position within the interior of the object and could provide reflections and / or diffractions at the first predetermined position and / or wherein in step a. the first ultrasound signal is transmitted and in step b. ultrasound is received such as in step b. reflections and / or diffractions at the first predetermined position of the first ultrasound signal are received, the first ultrasound signal after it has provided the reflections and / or diffractions at the first predetermined position at least once within the object on the at least one predetermined reflection surface 10 before being received by the plurality of ultrasound receivers, wherein in step c. the receiving signals are processed according to the principle of inverse wave field extrapolation while in the inverse wave field extrapolation, which is carried out in the processing, said at least one reflection on the at least one predetermined reflection surface is taken into account.

Method according to claim 1, characterized in that in step a. The first ultrasound transmitter is positioned relative to the object such that the first ultrasound signal, after it is transmitted, reflects at least one time within the object on the at least one predetermined reflection surface before it reaches the first predetermined position within the interior of the object and could provide reflections and / or diffractions at the first predetermined position and / or wherein in step a. and step b. the first ultrasound transmitter and the plurality of ultrasound receivers 25 are positioned relative to the object such that if the first ultrasound signal provides reflections and / or diffractions at the first predetermined position, then it will reflect at least once within the object at the at least one predetermined reflection surface before it is received by the plurality of ultrasound receivers. 30

Method according to claim 1 or 2, characterized in that in step a. The first ultrasound transmitter is positioned relative to the object such that the first ultrasound signal, after it is transmitted, reflects at least once within the object on the at least one a predetermined reflection surface before it could provide reflections and / or diffractions for the first time at the first predetermined position and / or wherein in step a. and step b. the first ultrasound transmitter and the plurality of ultrasound receivers are positioned relative to the object such that if the first ultrasound signal provides reflections and / or diffractions for the first time at the predetermined position, it will then reflect at least once within the article on the at least one predetermined reflection surface before it is received by the plurality of ultrasound receivers.

Method according to one of the preceding claims, characterized in that the position of the at least one predetermined reflection surface relative to the ultrasound transmitter used in step a. And / or the position of the at least one predetermined reflection surface relative to the plurality of ultrasound receivers used in step b. is known and is used in step c. wherein, for example, the position of the at least one reflection surface could be known by performing measurements on the object using known techniques or could be known from existing information about the object.

A method according to any one of the preceding claims, characterized in that the shape of the at least one predetermined reflection surface is known and is used in step c.

6. Method as claimed in any of the foregoing claims, characterized in that, in step a. The first ultrasound signal is transmitted such that it reflects at least once within the object on the at least one predetermined reflection surface before it reaches the first predetermined position achieved in which subsequently in step b. as in step b. reflections and / or diffractions at the first predetermined position of the first ultrasound signal is received, the first ultrasound signal after it has provided the reflections and / or diffractions at the first predetermined position within the object on no reflection surface of the object reflects before being received by the plurality of ultrasound receivers; or in step a. the first ultrasound signal is transmitted such that it does not reflect within any object on any reflection surface of the object 10 before it reaches the first predetermined position, then in step b, as in step b. reflections and / or diffractions at the first predetermined position of the first ultrasound signal are received, the first ultrasound signal after it has provided the reflections and / or the diffractions at the first predetermined position does reflect once within the object on the at least one predetermined reflection surface of the object before it is received by the plurality of ultrasound receivers; or in step a. the first ultrasound signal is transmitted such that it reflects once within the object on the at least one predetermined reflection surface before it reaches the first predetermined position, then in step b., as in step b. reflections and / or diffractions at the first predetermined position of the first ultrasound signal are received, the first ultrasound signal after it has provided the reflections and / or the diffractions at the first predetermined position does reflect once within the object on a first predetermined reflection surface of the object and then once inside the object at a second predetermined reflection surface of the object before it is received by the plurality of ultrasound receivers, preferably the at least one predetermined reflection surface 30 used in step a. is the same as one of the first predetermined reflection surface and the second predetermined reflection surface used in step b; or in step a. the first ultrasound signal is transmitted such that it reflects once within the object on a first predetermined reflection surface of the object and then once within the object on a second predetermined reflection surface of the object before it predetermined position whereupon then in step b., as in step b. reflections and / or diffractions at the first predetermined position of the first ultrasound signal are received, the first ultrasound signal 10 after it has provided the reflections and / or the diffractions at the first predetermined position once reflects within the object on the at least one predetermined reflection surface of the article before it is received by the plurality of ultrasound receivers, preferably the at least one predetermined reflection surface used in step b. is the same as one of the first predetermined reflection surface and the second predetermined reflection surface used in step a .; or in step a. the first ultrasound signal is transmitted such that it reflects once within the object on the at least one predetermined reflection surface before it reaches the predetermined position and then in step b., as in step b. reflections and / or diffractions at the first predetermined position of the first ultrasound signal are received, the first ultrasound signal after it has provided the reflections and / or the diffractions at the first predetermined position once within the object on a first predetermined reflection surface of the object before it is received by the plurality of ultrasound receivers, preferably the at least one predetermined reflection surface used in step a. is the same as the first predetermined reflection surface used in step b.

7. Method as claimed in any of the foregoing claims, characterized in that, the object is in the form of a plate with a first outer wall and a second outer wall opposite each other, wherein in step a. The ultrasound signals are transmitted within the object of the first outer wall of the object and wherein in step b. the ultrasound signals are received from the object on the first outer wall of the object and / or the second outer wall of the object.

A method according to claim 7, characterized in that the first outer wall 10 of the object or the second outer wall of the object forms the at least one predetermined reflection surface and / or wherein the first outer wall of the object forms the first predetermined reflection surface and / or the second outer wall of the object forms the second predetermined reflection surface. 15

A method according to any one of claims 7-8, characterized in that the first outer wall and the second outer wall are each substantially flat surfaces that extend parallel to each other in the main pocket.

A method according to any one of claims 1-6, characterized in that the object is in the form of a house wall with a first outer wall and a second outer wall which are substantially concentric to each other, wherein in step a. The ultrasound signals are transmitted inwards the object from the first outer wall and / or the second outer wall and wherein in step b. The ultrasound signals from the object are received on the first outer wall and / or the second outer wall.

11. Method as claimed in claim 10, characterized in that the first outer wall of the object or the second outer wall of the object forms the at least one predetermined reflection surface and / or wherein the first outer wall of the object forms the first predetermined reflection surface and / or the second outer wall of the object forms the second predetermined reflection surface.

A method according to claim 10 or 11, characterized in that the first outer wall of the tube is formed by an outer wall of the tube and that the second outer wall of the tube is formed by an inner wall of the tube, or in that the first outer wall of the tube is formed by an inner wall of the tube and that the second outer wall of the tube is formed by an outer wall of the tube.

13. Method according to at least claim 6 and according to claim 7 or 10, characterized in that, in step a. The ultrasound signals are transmitted to the inside of the object from the first outer wall of the object and wherein in step b. the ultrasound signals are only received from the object on the first outer wall of the object and wherein: the second outer wall forms the at least one reflection surface used in step a .; or 20. the second outer wall forms the at least one reflection surface used in step b .; or - the second outer wall forms the at least one predetermined reflection surface used in step a., the first outer wall forms the first predetermined reflection surface used in step b. and the second outer wall forms the second predetermined reflection surface used in step b; or - the second outer wall forms the first predetermined reflection surface used in step a., the first outer wall forms the second predetermined reflection surface used in step a. and the second outer wall forms the at least one predetermined reflection surface that is used. is described in step b .; or - the outer wall forms the at least one predetermined reflection surface used in step a. and the second outer wall forms the first predetermined reflection surface used in step b.

Methods according to one of claims 7-13, characterized in that: in step a. Only the second outer wall is used as the at least one predetermined reflection surface and that in step b. no reflection surface 10 is used; or - in that in step b. only the second outer wall is used as the at least one predetermined reflection surface and that in step a. no reflection surface is used; or in that in step a. only the second outer wall is used as the at least one predetermined reflection and that in step b. the first outer wall is used as the first predetermined reflection surface and the second outer wall is used as the second predetermined reflection surface; or - in that in step b. only the second outer wall is used as the at least one predetermined reflection surface and that in step a. the first outer wall is used as the second predetermined reflection surface and the second outer wall is used as the first predetermined reflection surface; or 25. in that in step a. only the second outer wall is used as the at least one predetermined reflection surface and that in step b. only the second outer wall is used as the first predetermined reflection surface.

A method according to any one of the preceding claims, characterized in that the predetermined position is relatively close to the outer surface of the object, in particular wherein the predetermined position is in an area extending from the first outer wall to the second outer wall as indicated in claim 7 or 10 over a distance of less than 50%, preferably less than 25%, more preferably less than 12.5% of the distance between the first and second surface.

16. Method as claimed in any of the foregoing claims, characterized in that the predetermined position lies under a weld cap or under an uneven or inaccessible surface of the object.

A method according to any one of the preceding claims, characterized in that, in step b. the plurality of ultrasound receivers is spread over a two-dimensional array relative to the surface of the object from which the ultrasound signals are received.

18. Method as claimed in any of the foregoing claims, characterized in that, in step a. The first ultrasound signal is transmitted within the object 20 via an intermediary medium, such as a wedge, liquid or flexible cushion, in particular a plastic wedge and wherein possible in step b. the ultrasound receiving signals are received by an intermediate medium, such as a wedge, liquid or flexible cushion, in particular a plastic wedge.

A method according to claim 18, characterized in that the intermediate medium used in step a. Is designed such that the first ultrasound signal within the object comprises shear waves.

20. A method according to any one of the preceding claims, characterized in that step a. Is repeated for another ultrasound transmitter of the first group of ultrasound transmitters, wherein step b. is repeated for each repeated step a. using a plurality of ultrasound receivers from the group of ultrasound receivers and wherein step c. is performed on the basis of the collection of reception signals obtained in steps b. which 5 have been executed.

A method according to any one of the preceding claims, characterized in that step a. Is repeated for another ultrasound transmitter of the first group of ultrasound transmitters, wherein step b. is repeated for each repeated step a. using a plurality of ultrasound receivers from the group of ultrasound receivers and wherein step c is performed for each repeated step b.

22. A method according to any one of the preceding claims, characterized in that, step a. Is repeated for each ultrasound transmitter of the group of ultrasound transmitters, wherein step b. is performed for each step a. which has already been performed using a plurality of ultrasound receivers from the group of ultrasound receivers wherein step c. is performed on the basis of the collection of reception signals obtained in steps b. 20 which have been carried out.

A method according to any one of the preceding claims, characterized in that step a. Is repeated for each ultrasound transmitter of the group of ultrasound transmitters, wherein step b. is performed for each step a. which has already been performed using a plurality of ultrasound receivers from the group of ultrasound receivers wherein step c. is performed for each step b. which has already been implemented.

A method according to any one of the preceding claims, characterized in that, in step b. each ultrasound receiver from the group of ultrasound receivers is used to receive the ultrasound signals.

A method according to any one of the preceding claims, characterized in that, step c. comprising calculating for the predetermined position within a predetermined area, and based on the reception signals obtained in step b., ultrasound signals at this position which the reception signals obtained in step b. respectively, wherein said calculation is based on the principle of inverse wave field extrapolation, the method further comprising repeating step c. for a plurality of predetermined positions within the predetermined area to obtain information for constructing an image of the predetermined area.

The method according to claim 25, characterized in that, in step c. based on all reception signals obtained in step b. said calculated signals are calculated based on the principle of inverse wave field extrapolation.

A method according to claim 25 or 26, characterized in that, in step c. for each receive signal obtained in step b. one of said ultrasound signals is calculated based on the principle of inverse wave field extrapolation.

Methods according to claim 27, characterized in that, in step c. for each receive signal obtained in step b. said calculated ultrasound signal is calculated for a moment in time at which the calculated ultrasound signal forms a response to the transmitted ultrasound signal in step a.

A method according to any one of claims 25-28, characterized in that, in step c. based on the reception signals obtained in step b. new corresponding reception signals are calculated with the new corresponding reception signals now being a presumed result of a virtual receiver and virtual transmitter being present at the predetermined position whereby characteristics of the calculated new corresponding reception signals are selected which correspond to an assumed travel time of the virtual source to the virtual receiver that is zero. 10

The method according to any of claims 25-29, characterized in that, in step c. based on the reception signals obtained in step b. new corresponding receive signals are calculated with the new corresponding receive signals now being an assumed result of a virtual receiver and virtual transmitter being present at the predetermined position with the new corresponding receive signal being integrated across all frequencies in the frequency domain representation of the new corresponding receive signal for the obtaining the calculated ultrasound signal for a moment in time at which the calculated ultrasound signal is a response of the transmitted ultrasound signal in step a.

A method according to any of claims 25-30 and according to claim 18, characterized in that, step c. first comprises calculating the propagation of the transmitted ultrasound signal through the intermediate medium, using the principle of forward wave field extrapolation and then calculating the continued propagation of the transmitted ultrasound signal through the object using the principle of forward wave field extrapolation and where step c. possibly calculating based on the reception signals of first the propagation of the ultrasound signals through the intermediate medium using the principle of inverse wave field extrapolation and then calculating the preceding propagation of the ultrasound signals by the object using the principle of inverse wave field extrapolation as in step b. the ultrasound signals are received by the intermediate medium.

The method according to any of claims 25-31, characterized in that the predetermined position within the image is represented by a pixel with a color and / or intensity corresponding to a combination, eg the sum, mean, mean, minimum or maximum of the calculated values of the plurality of ultrasound signals calculated in steps c. for a predetermined position.

A method according to any one of claims 25-32, characterized in that, the calculated ultrasound signal is represented by a complex number comprising the amplitude and phase of the calculated ultrasound signal at said moment in time.

The method according to any of the preceding claims, characterized in that the ultrasound signal transmitted in step a. Is an ultrasound pulse or a plurality of ultrasound pulses spread over time.

35. A method according to any one of the preceding claims, characterized in that each transmitter forms one of the receivers and vice versa.

A system for carrying out a method according to any one of the preceding claims, comprising a group of transmitters, a group of receivers and control means communicatively connected to the group of transmitters and the group of receivers wherein the control means are arranged to perform step c. of the method.

The system according to claim 36, characterized in that the control means 5 are also arranged to carry out step a. And step b. to be carried out.